Question: Simplify the following expression: $x = \dfrac{p^2 - 9p + 20}{p - 4} $
First factor the polynomial in the numerator. $ p^2 - 9p + 20 = (p - 4)(p - 5) $ So we can rewrite the expression as: $x = \dfrac{(p - 4)(p - 5)}{p - 4} $ We can divide the numerator and denominator by $(p - 4)$ on condition that $p \neq 4$ Therefore $x = p - 5; p \neq 4$